An incidence theorem in higher dimensions

Klazar comments on the article by Solymosi et al. on an incidence theorem in higher dimensions. He notes that the authors generalize (a weaker form of) the Szemeredi-Trotter theorem that bounds the number of point-line incidences in the plane to points versus real algebraic varieties. The proof of t...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin (new series) of the American Mathematical Society 2019-07, Vol.56 (3), p.523
Main Author: Klazar, Martin
Format: Article
Language:English
Subjects:
Algebra
Incidence
Mathematical functions
Polynomials
Theorems
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Klazar comments on the article by Solymosi et al. on an incidence theorem in higher dimensions. He notes that the authors generalize (a weaker form of) the Szemeredi-Trotter theorem that bounds the number of point-line incidences in the plane to points versus real algebraic varieties. The proof of the main theorem is given in Section 5, the main tools being "the polynomial ham sandwich theorem and induction on both the dimension and the number of points". In addition to a comparison with existing results, Section 2 contains several applications of the main theorem. (Reprint)
ISSN:0273-0979
1088-9485
DOI:10.1090/bull/1671